At Large  February 17, 2021  Anna Claire Mauney

How Artists Used The Golden Ratio To Create Masterpieces

Uffizi Gallery, Florence Italy.

Leonardo da Vinci, Annunciation, c. 1472.

The golden ratio is an irrational number that approximately equals 1.618. For artistically minded people, the ratio—or better yet, the divine proportion—might be easier to understand visually.

Courtesy of Wikimedia Commons.

Lithuanian coin with the golden spiral.

This is easiest to demonstrate with the golden spiral, which is often depicted and constructed within a rectangular frame. The ratio between this rectangle’s length and width is that of the golden ratio.

The spiral is built by portioning the original rectangle into two pieces—a square and rectangle of the same proportional width and length. The process is repeated and the spiral is applied via quarter-circles that run from corner to corner of the squares created.

The result is technically not a truly logarithmic or golden spiral but it is a close approximation. More importantly, this is the type of process artists have used to visualize and apply the divine proportion to their paintings throughout the centuries.

Courtesy of Wikimedia Commons.

Luca Pacioli, Title page of Divina proportione, 1509.

According to historians, the golden ratio was first studied by ancient Greek mathematicians. While some believe the Grecians did associate the ratio with aesthetics and even applied it to achieve beauty—many argue it was intentionally used in the Parthenon—there is little evidence to support this.

Widespread artistic interest in the ratio—within Western circles—can, however, be justifiably associated with the publication of Divina proportione in 1509.

The book, written by mathematician Luca Pacioli and illustrated by Leonardo da Vinci, is widely lauded for its clear writing and stunning illustrations. Many believe these qualities allowed the book to reach and occupy artistic circles.

There is no doubt that the golden ratio runs rampant through the art of the sixteenth century and on. The most evident manifestation of the ratio lies in the composition of paintings and cutting of canvases. One only needs to envision the golden spiral atop any number of compositions from this era and beyond.

Obviously, Da Vinci frequently employed the golden ratio but so did many of his contemporaries as well as artists born centuries later.

Uffizi Gallery, Florence Italy.

Raffaello Sanzio,Madonna of the Goldfinch, 1505 - 1506.

In Raffaello Sanzio’s Madonna of the Goldfinch, the principles of the golden ratio can be seen throughout the painting. The three largest quarter circles manifest in Madonna’s upper-left side, the far leg of John the Baptist, and the feet of the Christ Child. These three arcs work together to lead the eye through the painting and the ratio as a whole gives the image a sense of balance and so-called divine proportion.

Geometric shape rendered as though it was constructed with bars in a hollow, cage-like fashion.
Courtesy of Wikimedia Commons.

Leonardo da Vinci, Rhombicuboctahedron from Divina proportione, 1509.

Last super painted inside a more realized version of Leonardos Rhombicuboctahedron
Courtesy of WikiArt.

Salvador Dalí, The Sacrament of the Last Supper, 1955.

Other mathematical principles covered in Pacioli’s Divina proportione have also appeared in art through the centuries. See Da Vinci’s illustration, Rhombicuboctahedron, and Salvador Dalí’s 1955 take on The Sacrament of the Last Supper.

About the Author

Anna Claire Mauney

Anna Claire Mauney is Managing Editor for Art & Object. A writer and artist living in North Carolina, she is interested in illustration, the 18th-century, and viceregal South America. She is also the co-host of An Obsessive Nature, a podcast about writing and pop culture.

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